Police believe they have done enough to avert the government’s threat to pass new laws outlawing the abuse of stop and search powers, despite new figures showing that black people are six times more likely to be targeted by officers than white people.

The official figures show a big fall in police use of stop and search for all ethnic groups. While more than eight in 10 incidents still lead to no arrest, changes appear to have reduced the police time wasted and infringements on the rights of innocent people.

However, the power is being used more disproportionately against black people than white people and that disparity grew in the past year. A black person was six times more likely to be stopped and searched by police than a white person, up from four times more likely the year before.

The government has threatened to pass new laws if the police do not reform sufficiently, but the issue now is whether ministers view the progress as sufficient.

Adrian Hanstock, the national police lead on stop and search, told the Guardian that enough had been done. “I think we’ve started to demonstrate the changes that the government had asked for,” he said.

“Have we done enough to demonstrate commitment, the will to change and ability to change? Yes, I think we have, because the legislation would be being laid now, they would not have waited four years.”

In 2015-16, the number of stops fell 28%, to 386,474, with 16% leading to an arrest, suggesting that officers are using the powers in a more focused way than in previous years.

However, people from black and minority ethnic (BME) groups as a whole were almost three times more likely to be stopped than white people.

The Home Office commentary accompanying the statistics pointed out that the Metropolitan police’s higher use of stop and search than any other force skewed the figures, because much of Britain’s BME population lives in London.

The Met stopped 18 out of every 1,000 people in their policing area, more than twice the England and Wales average of seven stops per 1,000.

“MPS [the Met] account for a large proportion (40%) of stops and searches in England and Wales. As the force has a considerably larger BME population than other parts of the county, data for MPS can skew the data at a national level when considering the ethnicity of those stopped,” the report said.

The home secretary, Amber Rudd, said the disproportionate stops directed against black people were due to prejudice.

“While today’s statistics show that our stop and search reforms are working, with a continuing fall in the overall number of stops and the highest ever recorded arrest rate, it is completely unacceptable that you are six times more likely to be stopped and searched if you are black than if you are white,” she said.

“I am clear that, in a Britain that works for everyone, no one should be stopped on the basis of their race or ethnicity.”

The Home Office did not answer whether it believed police had achieved enough to lift the threat of legislation, but it did say the police inspectorate would examine forces next year on stop and search.

The Conservatives hope one byproduct of their words and actions on race and the criminal justice system will be an increase in their low share of the increasingly important BME vote.

Diane Abbott, the shadow home secretary and one of Britain’s most senior black politicians, said: “BME people have long been disproportionately subjected to stop and search. There is no objection to evidence-based stops, but what inflames the relationship between the community and the police is the abuse of stop and search.

“It poisons relationships between young people in inner cities and the police. Unless you have a young male family member who is repeatedly stopped and searched, it is difficult to appreciate the damage it can do.

“Tensions between the community and police led to the riots of the 80s and were cited as a reason for more recent public disturbances.”

A spokesperson for Black Lives Matter UK said the latest figures showed the ineffectiveness of stop and search reform. “These stats show that the new ‘intelligence-led’ stop and searches are really just prejudice-led. This is institutional racism, not just bad apples. We want this power scrapped and police forces held properly accountable.”

Stafford Scott, the coordinator of Tottenham Rights, which challenges institutional racism, said this interpretation chimed with the experience of the young people he worked with in north London. “This is part of the power that police have used like a blunt instrument to contain and control our community,” he said.

Scott said the increase in stop and search disproportionality showed that police intelligence, the supposed basis for the use of stop and search in London, unfairly targeted black youths while letting suspects from other communities off the hook.

“In a borough like Haringey, where the Turkish gangs are, it’s only black kids that are on the Matrix [the Met’s gangs database]. [The police] say they are gangsters and then stop and search them all the time,” Scott said.